At least three people died in a day of violence in Kiev on Wednesday, as an opposition leader said he was willing to face "a bullet in the forehead" if President Viktor Yanukovych did not launch snap elections.

A three-hour meeting between the embattled president and the three main political opposition leaders ended without a deal, leaving the capital braced for intensified violence.

Two men died from bullet wounds on Wednesday, according to Ukraine's general prosecutor, while the third died after falling from a rooftop while fighting with police. Protesters report that dozens of people have been seriously injured during the clashes, which have been running since Sunday evening.

Parts of central Kiev resembled a battlefield, with police firing rubber bullets and wielding truncheons, while protesters lobbed molotov cocktails. The two men who were shot were killed with live ammunition, the authorities admitted. As night fell people drove cars filled with used tyres up to the main front line and made a giant bonfire, throwing molotov cocktails from behind the flames.

Former heavyweight boxing champion Vitali Klitschko, now an opposition politician, said Yanukovych had 24 hours in which to call snap elections, and demanded another meeting with the president on Thursday. If this did not happen, he said, the opposition would "go on the attack". His words drew loud cheers from the crowd on Independence Square, hub of the protests.

"If we have to fight, I will fight together with you. If we have to face bullets, I will face bullets," Klitschko told the crowd.

Police fire at protesters in Kiev: Photograph: Evgeny Feldman/AP

Arseniy Yatsenyuk, who represents the party of jailed former prime minister Yulia Tymoshenko and attended the meeting with Yanukovych, also had fighting words for the tens of thousands of demonstrators on Independence Square: "Tomorrow we will go forward together. And if it's a bullet in the forehead, then it's a bullet in the forehead – but in an honest, fair and brave way."

The opposition leaders initially condemned attacks by protesters on riot police when they began on Sunday night, saying they were carried out by "provocateurs". But as the mood has become more radical, they have come under pressure to take a more decisive stance.

Yanukovych issued a statement saying he did not want bloodshed or the use of force, but the government does not appear ready to compromise. Prime minister Mykola Azarov called the protesters "terrorists". He said those who died were responsible for their fate and insisted the government had no option but to use force.

He later left Kiev for Davos, where he was due to take part in a panel at the World Economic Forum on Friday. However, it emerged that after the deaths in Kiev his invitation to the panel, and to the forum itself, was rescinded.

Condemnation of the violence poured in from across the world. The US embassy in Kiev said it had revoked visas for a number of Ukrainian officials linked to police violence against demonstrators, and said Washington was considering taking further steps against the regime.